Each obviously has its advantages. I'm using RH 8.0 myself. I was actually pretty impressed with Lycoris desktop/LX from an ease-of-use standpoint. The downside with Lycoris is that it doesn't come with many of the things commonly found in other distros (Apache, MySQL, PostgreSQL, for example), and tutorials and RPMs for Lycoris are much less common than for distros that have been around longer.
Mandrake, unlike RH, includes read-only support for NTFS, which is worth considering if you'll ever dual boot with Windows NT/2000/XP. As I said, though, I'm using Redhat 8.0; I recompiled the kernel with NTFS support with relatively little trouble. There are tutorials around for doing exactly that if you're interested.
Other little nuisances with RH include the lack of mp3 support, but that can be fixed in about ten seconds.
I find the organization of the Redhat whatever menu (the Start Menu/Apple Menu wannabe) downright bizarre, and I'm not entirely crazy about Nautilus as a file manager compared to Konqueror, but you can switch to KDE if you want to anyway.
That's my two cents worth for the moment.